Mercury prizewinning rapper Speech Debelle is exhausted. She won the Mercury prize for her debut album, Speech Therapy, less than 24 hours ago and her day is jam-packed with interviews, phone calls and taxis. "That's the first thing to have passed my lips since last night," she says, grimacing at a cup of pallid-looking coffee. For someone who has not yet been to bed, Debelle looks remarkably composed, but then this 26-year-old south Londoner is made of strong stuff.

Born in London to middle-class Jamaican parents, Debelle (her real name is Corynne Elliot) would rap for her mates in lessons at the age of 13. Repeatedly suspended from her school Harris City Academy for being a difficult pupil, Debelle used to hang around and smoke cannabis on the steps of Crystal Palace park. At 18, she started writing down her feelings and experiences; which would prove the origins of her debut album. Yet any hopes of getting into the music industry stalled when, aged 19 and after constant fights with her mother, Debelle left home.

She spent the next four years homeless, living in and out of hostels, sleeping on friend's sofas. In her debut single, Searching, she writes about that life: "2am in my hostel bed/My eyes them red, my belly ain't fed/I got butter but I ain't got bread/And I'm smoking on my last cigarette." Clearly, the album is called Speech Therapy for a reason – although, on the morning after the ceremony, dressed in a black hoodie with black sequined leggings and £20,000 richer, Debelle doesn't want to dwell on the darker moments of her past.

At the age of 23 – older, wiser and presumably calmer – she moved back in with her mother, and in 2005 went in for her first meeting with the independent label Big Dada (which also looks after the UK rapper Roots Manuva), coolly informing the people there that she wanted to be a "hip-hop Tracy Chapman".

When she is rapping and singing, Debelle's voice is soft, young and feminine. There is a vulnerability to her lyrics, which comes across even more clearly in person. But despite the big laugh and warm smile, there's a lot going on under the surface: you suspect she has seen many things she wishes she hadn't in her life, and has probably done the occasional thing she shouldn't have. In the album's title track, Debelle apologises to her mother for the hurt she has caused her:

"I'm sorry Mum for all the times that I made you cry/And it's been said before in songs but you are my life . . . And nobody's gonna hurt you ever as long as this sun shines/And hell would have to freeze over before I take that back/This is my speech therapy, this isn't rap."

Then in Daddy's Little Girl, the song she regards as the most hard-hitting, she raps about the anger she feels towards her father, who walked out when Debelle was six years old. The whole album is an honest, intimate account of one woman's struggle to find a place in society, but it is also touchingly playful and uplifting.

According to her record company, before she won the Mercury prize Debelle's album had sold less than 5,000 records, which, while not bad for a small label with no TV advertising, is still pretty small beans – probably the lowest figure for a winner of the award. Yesterday, it was reported that there had already been a 4,000% increase in sales . . .

HP: So how did you feel when they read your name out?

SD: Relief. Relief that after all this time I've been saying how confident I was of winning, it actually did happen; otherwise I'd have looked pretty silly. I was emotional up there – I guess it's a feeling of acceptance.

It did seem like you had a lot of confidence beforehand. That wasn't all front, then?

No, it was real. I was confident in the album, I thought it was a brilliant album.

But Jools Holland said he was surprised you won.

Jools Holland needs to put me on his show now, that's what Jools Holland needs to do.

Did you cry last night?

I cried a little bit when they said my name – then my makeup artist said, "Don't you dare." He stopped me.

Where does your name come from?

My gran has a fashion label called Madame De Belle – her name is Deeble and she changed it to Debelle for the label, so I've grown up answering the phone: "Hello, Madame De Belle designs." When I needed to come up with a name, I already had Speech and Debelle seemed to fit neatly. Then I found out that in French it means voice of the beautiful or something like that.

Do you consider yourself a hip-hop artist?

I'm a rapper, an MC. I love the art of MCing, some of my favourite songs are by rappers – but I have a lot of other interests as well, and I think that shows on the album.

When you first sent your stuff to your record label, you mentioned Tracy Chapman . . .

Yes, at the first meeting about the album I told them, "I think it's like a hip-hop Tracy Chapman." They should have said OK, thanks for seeing us, don't let the door hit you on the way out – most labels would – but they didn't, they said OK, let's try it, let's see what happens.

It's also quite a poetic album – who were your other influences on it? Meshell Ndegeocello, particularly her album Bitter; the DMX song Slippin'; Tupac's Brenda's Got a Baby . . . it was particular songs. And Michael Jackson. Actually, Michael Jackson's song Human Nature turned into Daddy's Little Girl, that was the song we were trying to recreate. If you play those two songs together, the beginning is exactly the same.

Didn't you recently say that Michael Jackson was like Jesus?

Yes, but I don't know if it came across how I wanted. Actually I'm not sure how I wanted it to come across, I just threw it out there. I think the stories of Michael Jackson and Jesus are very similar – the only thing I know for a fact is that I've seen Michael Jackson, but I've never seen Jesus.

Are you religious, then?

Well I believe in good and evil inside everybody; I think we're all capable of great things and we're all capable of terrible things.

Political?

I'm socially political. I know the difference between politics and politricks.

A lot of people are saying the black community is in crisis. What do you think?

I don't know what it means, "in crisis".

That with the kids it's all about guns and gangs, and that parents don't stay together.

Well that's true, but you have to remember that burglary is a crime mostly committed by young white men; paedophilia is a crime mostly committed by white men; Timothy McVeigh [the Oklahoma bomber] killed one hundred and something people . . .

A lot has also been made about the time you spent living in hostels. Is it weird for you to talk about that?

Yes, so I'm going to stop. I decided that when I won the Mercury. I've spoken about it enough now, and it's easy for things to become glamorised. There's nothing nice about it, so there's no point in me keeping on saying it. I've made the point, raised it in people's consciousnesses, but I'm not going to use that to sell records.

How did you end up in those hostels?

It's just life, life is like that.

You said last night that watching Ms Dynamite win the Mercury prize in 2002 was a big inspiration for you.

Definitely. When she got it I thought, well, I can get one too.

But that's still quite a long time between black female winners.

True. It's weird because me, Ms Dynamite and Dizzee Rascal all have very different styles of music; the only thing that puts us together is the colour of our skin. None of us really sound alike, yet we're still being moulded together – it's sort of like, "You can't tell the difference in the dark."

Has black music got to where it needs to go now?

I'm not satisfied yet, so I don't think so.

Your lyrics are often quite emotional. How will you find being asked about all that stuff in interviews?

I've seen interviews with some artists where they just say they don't want to talk about it, but to me it's sincere and it's the truth, so I'm not going to feel worried.

What's the most hard-hitting song on your album?

For social reasons, Daddy's Little Girl. It's a letter to my dad letting him know what it feels like to be abandoned. There's anger and pain.

Has he been in touch?

No, I haven't spoken to him. I will do though, no doubt.

Anyone super-famous been in touch?

Nikki from Big Brother texted me the other day to say good luck. And I want to thank Thandie Newton for saying my album was one of her favourites.

Is there anything you're worried about, now you've had this success?

The lack of sleep I might be getting.

What about tall poppy syndrome?

I'm just watching all of you lot [the media]. It's easy for people to get delusional when they are constantly being asked to talk about themselves, and they believe it. No offence or anything but I'm looking at you lot like, whatever, knock yourselves out.

Where will you put the award?

My mum will probably take it. It's hers, I know that.

And what will you do with the money?

I haven't even put the cheque in the bank yet, so it better not bounce.

Is it one of those big cheques?

I though it was, but it's a real one. I thought I'd have to fill out forms, but it's actually a real cheque; I can walk into a bank and put it in.